Natural phantom dark energy, wiggling Hubble parameterH(z) and directH(z) data

Recent direct H ( z ) data indicate that the parameter H ( z ) may wiggle with respect to z . On the other hand, the luminosity distance data of supernovae flatten the wiggles of H ( z ) because of the integration effect. It is expected that the fitting results can be different in a model permitting a wiggling H ( z ) because the data of supernovae are degenerate in such a model. As an example the natural phantom dark energy is investigated in this paper. The dynamical property of this model is studied. The model is fitted by the direct H ( z ) dataset and the SNLS dataset, respectively. The results are rather different, as expected. The quantum stability of this model is also briefly discussed. We find that it is a viable model if we treat it as an effective theory truncated by an upper bound.